Defects Control Charts Using Interval-Valued Penthagorean Fuzzy Sets

Elif Haktanır; Cengiz Kahraman

doi:10.1007/978-3-030-51156-2_162

Defects Control Charts Using Interval-Valued Penthagorean Fuzzy Sets

Elif Haktanır^*, Cengiz Kahraman

^*Corresponding author for this work

Department of Industrial Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

Defects control charts are one of the attributes control charts which are constructed based on the number of defects on a product or in an inspection unit. Since the term ‘defect’ can be vague due to the subjective decisions of the quality control operator, it cannot be precisely defined. In such cases, fuzzy set theory can be used to add more information and flexibility to attribute based-process control. After the introduction of the ordinary fuzzy sets to the literature, it has been extended to many new types of fuzzy sets. One of the recent extensions, q-rung orthopair fuzzy sets, which is a generalization of intuitionistic fuzzy sets and Pythagorean fuzzy sets, provides a broader space to express ambiguous information, For the q-rung orthopair fuzzy sets the sum of the q^th power of the membership degree and the q^th power of the non-membership degree is equal to or less than one. In this study, the fifth power of the q-rung orthopair fuzzy sets is used to represent the impreciseness in the construction of the defects control charts and names as penthagorean fuzzy sets. An application in a TV production system is presented as an illustrative example.

Original language	English
Title of host publication	Intelligent and Fuzzy Techniques
Subtitle of host publication	Smart and Innovative Solutions - Proceedings of the INFUS 2020 Conference
Editors	Cengiz Kahraman, Sezi Cevik Onar, Basar Oztaysi, Irem Ucal Sari, Selcuk Cebi, A. Cagri Tolga
Publisher	Springer
Pages	1396-1406
Number of pages	11
ISBN (Print)	9783030511555
DOIs	https://doi.org/10.1007/978-3-030-51156-2_162
Publication status	Published - 2021
Event	International Conference on Intelligent and Fuzzy Systems, INFUS 2020 - Istanbul, Turkey Duration: 21 Jul 2020 → 23 Jul 2020

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	1197 AISC
ISSN (Print)	2194-5357
ISSN (Electronic)	2194-5365

Conference

Conference	International Conference on Intelligent and Fuzzy Systems, INFUS 2020
Country/Territory	Turkey
City	Istanbul
Period	21/07/20 → 23/07/20

Bibliographical note

Publisher Copyright:
© 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Attributes control charts
Defects control charts
Interval-valued penthagorean fuzzy sets
Intuitionistic fuzzy sets
q-rung orthopair fuzzy sets

Access to Document

10.1007/978-3-030-51156-2_162

Cite this

Haktanır, E., & Kahraman, C. (2021). Defects Control Charts Using Interval-Valued Penthagorean Fuzzy Sets. In C. Kahraman, S. Cevik Onar, B. Oztaysi, I. U. Sari, S. Cebi, & A. C. Tolga (Eds.), Intelligent and Fuzzy Techniques: Smart and Innovative Solutions - Proceedings of the INFUS 2020 Conference (pp. 1396-1406). (Advances in Intelligent Systems and Computing; Vol. 1197 AISC). Springer. https://doi.org/10.1007/978-3-030-51156-2_162

Haktanır, Elif ; Kahraman, Cengiz. / Defects Control Charts Using Interval-Valued Penthagorean Fuzzy Sets. Intelligent and Fuzzy Techniques: Smart and Innovative Solutions - Proceedings of the INFUS 2020 Conference. editor / Cengiz Kahraman ; Sezi Cevik Onar ; Basar Oztaysi ; Irem Ucal Sari ; Selcuk Cebi ; A. Cagri Tolga. Springer, 2021. pp. 1396-1406 (Advances in Intelligent Systems and Computing).

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abstract = "Defects control charts are one of the attributes control charts which are constructed based on the number of defects on a product or in an inspection unit. Since the term {\textquoteleft}defect{\textquoteright} can be vague due to the subjective decisions of the quality control operator, it cannot be precisely defined. In such cases, fuzzy set theory can be used to add more information and flexibility to attribute based-process control. After the introduction of the ordinary fuzzy sets to the literature, it has been extended to many new types of fuzzy sets. One of the recent extensions, q-rung orthopair fuzzy sets, which is a generalization of intuitionistic fuzzy sets and Pythagorean fuzzy sets, provides a broader space to express ambiguous information, For the q-rung orthopair fuzzy sets the sum of the qth power of the membership degree and the qth power of the non-membership degree is equal to or less than one. In this study, the fifth power of the q-rung orthopair fuzzy sets is used to represent the impreciseness in the construction of the defects control charts and names as penthagorean fuzzy sets. An application in a TV production system is presented as an illustrative example.",

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note = "Publisher Copyright: {\textcopyright} 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.; International Conference on Intelligent and Fuzzy Systems, INFUS 2020 ; Conference date: 21-07-2020 Through 23-07-2020",

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publisher = "Springer",

pages = "1396--1406",

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Haktanır, E & Kahraman, C 2021, Defects Control Charts Using Interval-Valued Penthagorean Fuzzy Sets. in C Kahraman, S Cevik Onar, B Oztaysi, IU Sari, S Cebi & AC Tolga (eds), Intelligent and Fuzzy Techniques: Smart and Innovative Solutions - Proceedings of the INFUS 2020 Conference. Advances in Intelligent Systems and Computing, vol. 1197 AISC, Springer, pp. 1396-1406, International Conference on Intelligent and Fuzzy Systems, INFUS 2020, Istanbul, Turkey, 21/07/20. https://doi.org/10.1007/978-3-030-51156-2_162

Defects Control Charts Using Interval-Valued Penthagorean Fuzzy Sets. / Haktanır, Elif; Kahraman, Cengiz.
Intelligent and Fuzzy Techniques: Smart and Innovative Solutions - Proceedings of the INFUS 2020 Conference. ed. / Cengiz Kahraman; Sezi Cevik Onar; Basar Oztaysi; Irem Ucal Sari; Selcuk Cebi; A. Cagri Tolga. Springer, 2021. p. 1396-1406 (Advances in Intelligent Systems and Computing; Vol. 1197 AISC).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Defects Control Charts Using Interval-Valued Penthagorean Fuzzy Sets

AU - Haktanır, Elif

AU - Kahraman, Cengiz

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AB - Defects control charts are one of the attributes control charts which are constructed based on the number of defects on a product or in an inspection unit. Since the term ‘defect’ can be vague due to the subjective decisions of the quality control operator, it cannot be precisely defined. In such cases, fuzzy set theory can be used to add more information and flexibility to attribute based-process control. After the introduction of the ordinary fuzzy sets to the literature, it has been extended to many new types of fuzzy sets. One of the recent extensions, q-rung orthopair fuzzy sets, which is a generalization of intuitionistic fuzzy sets and Pythagorean fuzzy sets, provides a broader space to express ambiguous information, For the q-rung orthopair fuzzy sets the sum of the qth power of the membership degree and the qth power of the non-membership degree is equal to or less than one. In this study, the fifth power of the q-rung orthopair fuzzy sets is used to represent the impreciseness in the construction of the defects control charts and names as penthagorean fuzzy sets. An application in a TV production system is presented as an illustrative example.

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KW - Interval-valued penthagorean fuzzy sets

KW - Intuitionistic fuzzy sets

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A2 - Cevik Onar, Sezi

A2 - Oztaysi, Basar

A2 - Sari, Irem Ucal

A2 - Cebi, Selcuk

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Haktanır E, Kahraman C. Defects Control Charts Using Interval-Valued Penthagorean Fuzzy Sets. In Kahraman C, Cevik Onar S, Oztaysi B, Sari IU, Cebi S, Tolga AC, editors, Intelligent and Fuzzy Techniques: Smart and Innovative Solutions - Proceedings of the INFUS 2020 Conference. Springer. 2021. p. 1396-1406. (Advances in Intelligent Systems and Computing). doi: 10.1007/978-3-030-51156-2_162

Defects Control Charts Using Interval-Valued Penthagorean Fuzzy Sets

Abstract

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Keywords

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